Calculating spatial weights in a radio communications system

ABSTRACT

A method and apparatus are provided that allows initial beamforming weights to be determined before timing or delay and frequency offset are known. According to one aspect of the present invention, the invention includes receiving a burst from a terminal at a set of spatial diversity antennas, the burst including a known training sequence and storing measurements of the received burst from each spatial diversity antenna corresponding to receive times within a selected analysis window. The invention further includes determining weights for each diversity antenna for at least a portion of the training sequence of the burst before timing for the burst has been determined, applying the determined weights to the stored measurements and determining timing for the burst based on the stored measurements to which the determined weights have been applied.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention applies to the field of spatial diversity radiocommunications systems and, in particular, to determining spatialweights for a received burst for which timing are unknown.

2. Description of the Prior Art

Mobile radio communications systems such as cellular voice and dataradio systems typically have several base stations in differentlocations available for use by mobile or fixed user terminals, such ascellular telephones or wireless web devices. Each base station typicallyis assigned a set of frequencies or channels to use for communicationswith the user terminals. The channels are different from those ofneighboring base stations in order to avoid interference betweenneighboring base stations. As a result, the user terminals can easilydistinguish the transmissions received from one base station from thesignals received from another. In addition, each base station can actindependently in allocating and using the channel resources assigned toit.

Such radio communications systems typically include a broadcast channel(BCH). The BCH is broadcast to all user terminals whether they areregistered on the network or not and informs the user terminals aboutthe network. In order to access the network, a user terminal normallytunes to and listens to the BCH before accessing the network. It willthen use the information in the BCH to request access to the network.Such a request typically results in an exchange of information about thenetwork using separate control and access channels and ends in the userterminal receiving an assignment to a particular base station.

While frequency and timing offset can sometimes be determined by a userterminal based on the BCH, the initial request for access is typicallytransmitted by the user terminal without any knowledge of its distanceto the base station, its timing delay or the direction to the basestation. In a spatial diversity multiple access system, the base stationcan enhance the capacity of the system by determining the position andrange to the user terminal as well as any other spatial parameters. Thetiming uncertainty of the arrival time of such request messages areproportional to the round trip delay encountered by messages travelingbetween the base station and the mobile terminal. For systems with ahigh coverage area per base station, this range and therefore the delayuncertainty may be very large. For example, a range of fifteen kmresults in a roundtrip delay time of around 100 microseconds.

In order to accurately resolve the access request and determine spatialparameters the timing or delay, frequency offset and spatial signatureof the user terminal's message are all desired. Typically, it ispreferred to accurately determine the timing, frequency offset and delaybefore the spatial signature is determined. This can create greatdemands on the processing resources of a base station and increase theamount of time required to generate a reply to the access request.

BRIEF SUMMARY OF THE INVENTION

A method and apparatus are provided that allows initial beamformingweights to be determined before timing or delay and frequency offset areknown. According to one aspect of the present invention, the inventionincludes receiving a burst from a terminal at a set of spatial diversityantennas, the burst including a known training sequence and storingmeasurements of the received burst from each spatial diversity antennacorresponding to receive times within a selected analysis window. Theinvention further includes determining weights for each diversityantenna for at least a portion of the training sequence of the burstbefore timing for the burst has been determined, applying the determinedweights to the stored measurements and determining timing for the burstbased on the stored measurements to which the determined weights havebeen applied.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example, and not by wayof limitation, in the figures of the accompanying drawings in which likereference numerals refer to similar elements and in which:

FIG. 1 is a simplified block diagram of a base station on which anembodiment of the invention can be implemented;

FIG. 2 is a block diagram of a remote terminal on which an embodiment ofthe invention can be implemented;

FIG. 3 is a diagram of an exemplary broadcast channel BCH burst;

FIG. 4 is a diagram of an exemplary configuration request CR burst;

FIG. 5 is a diagram of an exemplary training sequence in accordance withthe present invention;

FIG. 6 is a flow chart of an implementation of aspects of the presentinvention;

FIG. 7 is a graph of a search for a least squares error relative timing;and

FIG. 8 is a graph of a follow-up search for a least squares errorrelative timing.

DETAILED DESCRIPTION OF THE INVENTION Base Station Structure

The present invention relates to wireless communication systems and maybe a fixed-access or mobile-access wireless network using spatialdivision multiple access (SDMA) technology in combination with multipleaccess systems, such as time division multiple access (TDMA), frequencydivision multiple access (FDMA) and code division multiple access(CDMA). Multiple access can be combined with frequency divisionduplexing (FDD) or time division duplexing (TDD). FIG. 1 shows anexample of a base station of a wireless communications system or networksuitable for implementing the present invention. The system or networkincludes a number of subscriber stations, also referred to as remoteterminals or user terminals, such as that shown in FIG. 2. The basestation may be connected to a wide area network (WAN) through its hostDSP 231 for providing any required data services and connectionsexternal to the immediate wireless system. To support spatial diversity,a plurality of antennas 103 is used, for example four antennas, althoughother numbers of antennas may be selected.

A set of spatial multiplexing weights for each subscriber station areapplied to the respective modulated signals to produce spatiallymultiplexed signals to be transmitted by the bank of four antennas. Thehost DSP 231 produces and maintains spatial signatures for eachsubscriber station for each conventional channel and calculates spatialmultiplexing and demultiplexing weights using received signalmeasurements. In this manner, the signals from the current activesubscriber stations, some of which may be active on the sameconventional channel, are separated and interference and noisesuppressed. When communicating from the base station to the subscriberstations, an optimized multi-lobe antenna radiation pattern tailored tothe current active subscriber station connections and interferencesituation is created. Suitable smart antenna technologies for achievingsuch a spatially directed beam are described, for example, in U.S. Pat.Nos. 5,828,658, issued Oct. 27, 1998 to Ottersten et al. and 5,642,353,issued Jun. 24, 1997 to Roy, III et al.

The outputs of the antennas are connected to a duplexer switch 107,which in this TDD system is a time switch. Two possible implementationsof switch 107 are as a frequency duplexer in a frequency division duplex(FDD) system, and as a time switch in a time division duplex (TDD)system. When receiving, the antenna outputs are connected via switch 107to a receiver 205, and are mixed down in analog by RF receiver (“RX”)modules 205 from the carrier frequency to an FM intermediate frequency(“IF”). This signal then is digitized (sampled) by analog to digitalconverters (“ADCs”) 209. Only the real part of the signal is sampled.Final down-converting to baseband is carried out digitally. Digitalfilters can be used to implement the down-converting and the digitalfiltering, the latter using finite impulse response (FIR) filteringtechniques. This is shown as block 213. The invention can be adapted tosuit a wide variety of RF and IF carrier frequencies and bands.

There are, in the present example, four down-converted outputs from eachantenna's digital filter device 213, one per receive timeslot. Theparticular number of timeslots can be varied to suit network needs.While the present example uses four uplink and four downlink timeslotsfor each TDD frame, desirable results have also been achieved with threetimeslots for the uplink and downlink in each frame. For each of thefour receive timeslots, the four down-converted outputs from the fourantennas are fed to a digital signal processor (DSP) device 217(hereinafter “timeslot processor”) for further processing, includingcalibration, according to one aspect of this invention. Four MotorolaDSP56303 DSPs can be used as timeslot processors, one per receivetimeslot. The timeslot processors 217 monitor the received signal powerand estimate the frequency offset and time alignment. They alsodetermine smart antenna weights for each antenna element. These are usedin the spatial diversity multiple access scheme to determine a signalfrom a particular remote user and to demodulate the determined signal.

The output of the timeslot processors 217 is demodulated burst data foreach of the four receive timeslots. This data is sent to the host DSPprocessor 231 whose main function is to control all elements of thesystem and interface with the higher level processing, which is theprocessing which deals with what signals are required for communicationsin all the different control and service communication channels definedin the system's communication protocol. The host DSP 231 can be aMotorola DSP56303. In addition, timeslot processors send the determinedreceive weights for each user terminal to the host DSP 231. The host DSP231 maintains state and timing information, receives uplink burst datafrom the timeslot processors 217, and programs the timeslot processors217. In addition it decrypts, descrambles, checks error correcting code,and deconstructs bursts of the uplink signals, then formats the uplinksignals to be sent for higher level processing in other parts of thebase station. With respect to the other parts of the base station itformats service data and traffic data for further higher processing inthe base station, receives downlink messages and traffic data from theother parts of the base station, processes the downlink bursts andformats and sends the downlink bursts to a transmit controllermodulator,shown as 237. The host DSP also manages programming of other componentsof the base station including the transmit controllermodulator 237 andthe RF timing controller shown as 233.

The RF timing controller 233 interfaces with the RF system, shown asblock 245 and also produces a number of timing signals that are used byboth the RF system and the modem. The RF controller 233 reads andtransmits power monitoring and control values, controls the duplexer 107and receives timing parameters and other settings for each burst fromthe host DSP 231.

The transmit controllermodulator 237, receives transmit data from thehost DSP 231, four symbols at a time. The transmit controller uses thisdata to produce analog IF outputs which are sent to the RF transmitter(TX) modules 245. Specifically, the received data bits are convertedinto a complex modulated signal, up-converted to an IF frequency,4-times over-sampled, multiplied by transmit weights obtained from hostDSP 231, and converted via digital to analog converters (“DACs”) whichare part of transmit controllermodulator 237 to analog transmitwaveformns. The analog waveforms are sent to the transmit modules 245.

The transmit modules 245 up-convert the signals to the transmissionfrequency and amplify the signals. The amplified transmission signaloutputs are sent to antennas 103 via the duplexertime switch 107.

User Terminal Structure

FIG. 2 depicts an example component arrangement in a remote terminalthat provides data or voice communication. The remote terminal's antenna45 is connected to a duplexer 46 to permit antenna 45 to be used forboth transmission and reception. The antenna can be omni-directional ordirectional. For optimal performance, the antenna can be made up ofmultiple elements and employ spatial processing as discussed above forthe base station. In an alternate embodiment, separate receive andtransmit antennas are used eliminating the need for the duplexer 46. Inanother alternate embodiment, where time division diversity is used, atransmitreceive (TR) switch can be used instead of a duplexer as iswell-known in the art. The duplexer output 47 serves as input to areceiver 48. The receiver 48 produces a down-converted signal 49 whichis the input to a demodulator 51. A demodulated received sound or voicesignal 67 is input to a speaker 66.

The remote terminal has a corresponding transmit chain in which data orvoice to be transmitted is modulated in a modulator 57. The modulatedsignal to be transmitted 59, output by the modulator 57, is up-convertedand amplified by a transmitter 60, producing a transmitter output signal61. The transmitter output 61 is then input to the duplexer 46 fortransmission by the antenna 45.

The demodulated received data 52 is supplied to a remote terminalcentral processing unit 68 (CPU) as is received data before demodulation50. The remote terminal CPU 68 can be implemented with a standard DSP(digital signal processor) device such as a Motorola series 56300 DSP.This DSP can also perform the functions of the demodulator 51 and themodulator 57. The remote terminal CPU 68 controls the receiver throughline 63, the transmitter through line 62, the demodulator through line52 and the modulator through line 58. It also communicates with akeyboard 53 through line 54 and a display 56 through line 55. Amicrophone 64 and speaker 66 are connected through the modulator 57 andthe demodulator 51 through lines 65 and 66, respectively for a voicecommunications remote terminal. In another embodiment, the microphoneand speaker are also in direct communication with the CPU to providevoice or data communications.

The remote terminal's voice signal to be transmitted 65 from themicrophone 64 is input to a modulator 57. Traffic and control data to betransmitted 58 is supplied by the remote terminal's CPU 68. Control data58 is transmitted to base stations during registration, sessioninitiation and termination as well as during the session as described ingreater detail below.

In an alternate embodiment, the speaker 66, and the microphone 64 arereplaced or augmented by digital interfaces well-known in the art thatallow data to be transmitted to and from an external data processingdevice (for example, a computer). In one embodiment, the remoteterminal's CPU is coupled to a standard digital interface such as aPCMCIA interface to an external computer and the display, keyboard,microphone and speaker are a part of the external computer. The remoteterminal's CPU 68 communicates with these components through the digitalinterface and the external computer's controller. For data onlycommunications, the microphone and speaker can be deleted. For voiceonly communications, the keyboard and display can be deleted.

Broadcast Channel (BCH)

In one embodiment, the system of the present invention is initiated foreach user terminal or remote terminal from the broadcast channel BCHwhich is transmitted as a burst from the base station to all potentialuser terminals. The BCH burst, unlike the traffic channel bursts, istransmitted in all directions where user terminals may be, typicallyomnidirectionally but the specific beam pattern will depend on thenetwork. An example of a broadcast burst structure is shown in FIG. 3.The BCH communicates enough basic information to enable a subsequentexchange of configuration request CR and configuration message CMbetween the base station and the user terminal. The BCH also providesgeneral frequency offset and timing update information to all userterminals.

Table 1, below summarizes the content of an example of a BCH burst, asshown in FIG. 3.

TABLE 1 Duration Contents 10 μsec ramp - up 272 μsec  frequencycorrection training symbols f₁, f₂, . . . , f₁₃₆ 256 μsec  timingcorrection training symbols t₁, t₂, . . . , t₁₂₈ 16 μsec broadcastpreamble r₁, r₂, . . . , r₈ 512 μsec  information symbols h′₁, h′₂, . .. , h′₂₅₆ 10 μsec ramp - down 14 μsec inter-burst guard time

The frequency and timing correction training symbols can be setaccording to any one of many approaches well-known in the art. They canalso be combined, exchanged with a synchronization sequence oreliminated.

The broadcast information symbols are constructed from a 15-bitbroadcast message which is modulated and coded into a 256 bit sequence.The number of symbols as well as the structure and sequence oftransmitted bits can be varied to suit a wide variety of applications.The broadcast channel information symbols provide the information neededfor a user terminal to request a configuration message from the basestation.

Each broadcast message is mapped into a broadcast burst with theinformation shown below in Table 2.

TABLE 2 Broadcast Message Field # of Bits BStxPwr 5 BSCC 7 BSload 3Total 15

BStxPwr is the effective isotropic radiated power of the broadcastmessage. This number indicates the power transmitted by the base stationtaking into account the number of amplifiers and diversity antennasavailable at the base station.

BSCC is the base station color code, used by the user terminal to selecttraining data for uplink bursts and to distinguish broadcasts ofdifferent base stations.

BSload is an indication of the amount of unused capacity the basestation has.

In one embodiment, the network is designed to take maximal advantage ofspatial division multiple access technologies and particularly smartantenna array signal processing. To help maintain reliable spatialchannels in an extremely dense frequency reuse pattern, the network usestime division duplex TDMA where uplink and downlink transmissions arealways on the same frequency. In addition, because many user terminalsare single antenna and transmit and receive omnidirectionally, exceptfor the BCH, an uplink burst is always received before a downlink burstneeds to be sent. This allows downlink bursts to be more accuratelyspatially directed. An uplink training sequence is embedded in everyuplink burst to allow for moderately fast frequency hopping despite anydecorrelation of the spatial channel with frequency.

The frequency hopping sequence may be any one of many differentsequences well-known in the art. In one embodiment, the parameters ofthe frequency hopping scheme are initially unknown to the user terminal.This maximizes the flexibility of the network and increases theflexibility of the user terminal. As explained below, the frequencyhopping parameters are transmitted to the user in the CM burst.

In one embodiment, the BCH channel is shared by all base stations in thewireless communication system. Using the 7 bit BSCC, up to 128 basestations can be accommodated. The BCH is part of a time division duplexchannel with a repeating frame. The channel that includes BCH is asingle RF carrier frequency used for uplink and downlink. For high noiseenvironments or for increased robustness, the BCH can hop frequenciesaccording to a predetermined scheme or be repeated on several differentfrequencies. The repeating frame includes the downlink BCH for each basestation, labeled BS1 etc. as shown in Table 3 below. The next frameincludes the uplink Configuration Request CR, labeled CR1 etc. anddownlink Configuration Message CM, labeled CM1 etc. Each frame alsoincludes a number of reserved slots, shown as empty boxes below. Theseslots can be used for data traffic, if the broadcast channel is alsoused for traffic, for other control messages or reserved to reduceinterference on other channels in the network. In one embodiment, theother traffic channels hop frequencies around and through the BCH. Theframes are repeated for each respective base station 1 to 128 to build asuperframe as discussed in more detail below. After the last CM, CM128,the superframe repeats and begins again with the next superframe and theBCH for base station 1.

TABLE 3

In another embodiment, the BCH is on its own channel and CR and CM areon a separate control channel. Alternately, one BCH can be provided on aconstant frequency and a secondary BCH can be provided on anotherchannel with hopping frequency. The hopping channel is described in theCM.

Registration

In one embodiment of the present invention, a session begins when a userterminal seeks to register with a base station. The user terminal doesthis without knowing its relative position to the best station in termsof direction and distance (or range) to the base station (BS).Therefore, when the user terminal (UT or remote terminal or subscriberstation) requests registration using a configuration request (CR) burst,the base station receives the transmission from the user terminal with alarge timing uncertainty and unknown spatial parameters or weights whencompared to traffic bursts that already utilize timing advancedirectives from the base station.

Before registration, several user terminals may transmit CR burstsduring the same time slot to register with the same base station. CRbursts addressed to different base stations may also be received. Thebase station resolves these requests using spatial processing andmultiple antennas. By combining the multiple antenna measurements(beamforming) the base station minimizes the interference betweensignals and maximizes the signal-to-noise ratio (SNR) of each receivedburst.

Beamforming can be performed in a variety of ways. In one embodiment, atraining sequence is used with a least-squares cost function todetermine the weights for a beamformer. This allows signals to beclassified as desired or undesired. The training sequence-based approachuses an estimation of the timing and frequency offset of the CR burst.This estimation task can be performed by determining the least-squarescost for each timing and frequency hypothesis. This demands greatcomputational resources. Using a special sequence design and abeamforming algorithm that does not require a search over the entiretiming uncertainty range alleviates the computational load of the fullsearch. In one embodiment, since CR bursts have a high timinginaccuracy, a periodic training sequence is dedicated for CR burstsalone.

Configuration Request Burst Structure

A configuration request (CR) burst is transmitted by a user terminal(user terminal) in order to initiate communications or registration witha base station (base station). It is transmitted after gatheringinformation about the system by listening to (multiple) broadcastchannel (BCH) bursts. The CR burst, is the first communication from auser terminal to the base station and therefore, the user terminal doesnot have any information about its range to its selected base station.Accordingly timing, range, and spatial processing weights among otherthings are all unknown to the base station. An example of a CR burst isshown in FIG. 4.

The configuration request burst is composed of several fields as shownin FIG. 4 which are listed in Table 4. The durations are described interms of microseconds. In one embodiment, a symbol period is 2microseconds.

TABLE 4 Configuration Request (CR) Burst fields Duration Contents  10μsec ramp-up 240 μsec training symbols 164 μsec information symbols  10μsec ramp - down 106 μsec extra guard time  15 μsec inter-burst guardtime

The training symbols are allocated 240 microseconds in order to allowthe signal to be accurately received and demodulated before a userterminal has registered and has received any knowledge of the system.The training symbols are discussed in more detail below.

The 82 information symbols are constructed from the configurationrequest message using, for example, forward error correction coding. Inthe present embodiment, the CR burst is modulated using π/2-BPSKmodulation in order to decrease the peak-to-average ratio of thetransmitted waveform.

The information symbols of the present CR burst are mapped out as shownin Table 5, below. Any of the items listed below can be deleted andtransmitted later during the registration cycle or not at all based onthe needs of the system. CR is scrambled by a function of BSCC ensuringthat even if there is some interference from CRs sent to nearby basestations, the demodulation capture effect of the BSCC works out anycollisions. In one embodiment, the scrambling is performed by taking theencoded bit sequence and exclusive OR'ing it with the output of a linearfeedback shift register.

TABLE 5 Configuration Request Message Field # of Bits identity 8 utClass4 txPwr 5 Total 17

identity is a set of unique random bits for each user terminal thatdifferentiate simultaneous messages from multiple user terminals.Because of the randomness and large number of bits, it is unlikely thattwo user terminals will select the same identity code at the same time.

utClass identifies user terminal capabilities (highest modulation class,frequency hopping capabilities, etc.) This sequence identifies the typeof user terminal that sent the CR. A palmtop digital assistant mighthave different capabilities than a desktop computer with a fixeddedicated antenna. With utClass, the different capabilities can bedistinguished.

txPwr represents the power used by the user terminal to transmit theConfiguration Request burst. For example, user terminalpower=(2·txPwr−30) dBm.

In the present embodiment, the CR burst includes 106 microseconds ofextra guard time. As mentioned above, the CR burst is transmitted by auser terminal without any knowledge of the time required for the burstto travel to the base station. In the present embodiment, the desiredmaximum range from a user terminal to a base station is 15 km. The delayof the burst's reception at the base station includes the delay inreceiving the BCH from the base station. A user terminal at range R kmreceives the BCH burst(s) R/c seconds after they are transmitted by thebase station (c=3×10⁸ m/sec). When the user terminal decides to transmita CR burst, its signal will be delayed by another R/c seconds, so thatthe delay of the CR burst at the base station relative to base stationtime will be 2R/c seconds. To accommodate delays created by a maximumrange of 15 km, the guard period at the end of the CR burst time slotshould be at least 100 microseconds. In addition, in the presentembodiment, the user terminal randomly delays its CR burst transmissionfrom 0 to 9 symbols in order to reduce collisions with other userterminals that are sending CR bursts in the same slot and that may be atabout the same range from the base station. Therefore, a CR burst from adistant user terminal may arrive at the base station as much as 118microseconds late as compared to a user terminal that is very close tothe base station and that does not delay its CR burst transmission. Thisaccounts for the 106 microseconds of extra guard time that is allottedto the CR burst and the extra margin supplied by the 15 microseconds ofinter-burst guard time. With the inter-burst guard time 3 microsecondsof extra margin are allotted before the beginning of the next slot.

The present embodiment also includes an additional 15 microseconds ofinterburst guard time. This helps to confine the RF energy from the CRburst to the time-slot allocated for the CR burst in order not to createadjacent slot interference. The interburst guard time provides a totalguard time of 121 microseconds to reduce the likelihood that a CR burstwill extend into the next time slot.

The CR burst is sent on the control carrier, as an example, exactly 2265μsec after receipt of a downlink BCH burst. In this way, an otherwiseuninitialized user terminal can send CR without any knowledge of thefrequency hopping sequence parameters. As discussed above, the CR burstis shorter than a standard uplink time-slot to allow for unknowntime-of-flight from the user terminal to the base station and typicallyarrives late in the uplink time-slot receive window.

Training Sequences

In the present embodiment, known periodic training sequences are usedfor the training of base station beamformers in order to extract thedesired CR bursts in the presence of interference. The training sequenceincludes several periodic repetitions of a core sequence followed by amarker sequence. Alternatively, the marker sequence may precede therepetition of the core sequence. By repeating the core sequence, thesearch range for a least squares (LS) beamformer can be reduced to asingle repetition period of the training sequence. The period of thecore sequence is a compromise between the duration of the search rangeand the possibility of finding sequences of the specified period withgood autocorrelation and cross correlation properties. In the presentembodiment, constraints on the periodicity, mean, autocorrelation andcross correlation are used to define the core sequences of the trainingsequence for CR burst acquisition.

Periodicity: x(k+P)=x(k), in which x(k) is the periodic part of aπ/2-BPSK training sequence and P is the period of the sequence. In thepresent example, P=12 symbols.

Mean: the mean of the periodic sequence is constrained to be zero:${\frac{1}{P}\quad {\sum\limits_{k = 1}^{P}\quad {x\quad (k)}}} = 0.$

Autocorrelation: The out-of phase (symbol spaced) autocorrelation isbounded by 1/3, where τ is the phase offset of the out-of-phasesequence:${\frac{{\sum\limits_{k = 1}^{P}\quad {x*(k)\quad x\quad \left( {k + \tau} \right)}}}{\sum\limits_{k = 1}^{P}\quad {{x\quad (k)}}^{2}} \leq {1/3}},{\tau \neq 0}$

Cross correlation: Symbol spaced cross correlation between two candidateperiodic sequences x(k) and y(k) is bounded by 1/3:$\frac{{\sum\limits_{k = 1}^{P}\quad {x*(k)\quad y\quad \left( {k + \tau} \right)}}}{\sqrt{\sum\limits_{k = 1}^{P}\quad {{x\quad (k)}}^{2}}\quad \sqrt{\sum\limits_{k = 1}^{P}\quad {{y\quad (k)}}^{2}}} \leq 15_{1/3}$

At least two π/2-BPSK sequences conform to these constraints. Moresequences may be possible if the constraints are relaxed. These twosequences are used as the core 12 symbol sequence that is repeated toform the periodic training sequence as discussed below. They are:

s₁=[1,j,1,j,1,−j,−1,j,−1,−j,−1,−j]

s₂=[1,j,1,−j,−1,−j,1,j,−1,−j,−1,j]

The bounds on auto and cross correlations help to make delayed versionsof these sequences to appear partially uncorrelated to an LS beamformerwhich resolves them.

The two periodic sequences can be shared among base stations. In oneembodiment, depending on its color code, a base station will accept oneof the two core training sequences but not both. The user terminal willbe able to transmit the correct accepted sequence after learning thebase station color code from the broadcast (BCH) burst. This enables areuse pattern of 2. For reuse patterns greater than 2, some of theconstraints on the sequences can be relaxed to yield a larger set ofpossible periodic sequences to distribute among the base stations.

In an alternate embodiment, the user terminal selects which of the coresequences it will transmit. This can aid a base station in resolving twointerfering CR bursts. The core sequence can be selected based on aserial number, product number, ID number or other stored number of theuser terminal. For, example if the two sequences s₁ and s₂ above areavailable, the user terminal can read its serial number register. If theserial number is odd it selects sequence si and if the serial number iseven it selects S₂. In another embodiment, the user terminal cangenerate a random number from 1 to 2. If there are more than twosequences a greater range of random numbers can be generated. The randomnumber is then mapped into a list of sequences in order to select theperiodic sequence that is associated with the generated random number.

Transmitting CR Burst and Random Delay

In one embodiment, the base station transmits broadcast channel (BCH)bursts continuously over a pre-established known channel. To begin asession with a desired base station, an unregistered and unrecognizeduser terminal in an unknown location listens to the BCH bursts. From theBCH, it determines the base station with which wants to establishcommunications and selects an appropriate training sequence for thatbase station. It also selects a random number D between 0 and 9, andtransmits its CR burst after delaying it for D symbols. The number forthe delay can be selected as described above with respect to theperiodic training sequence. The user terminal can select an internalregister such as a Serial No. or Product ID No., that contains a numbergreater than 9 and use this as a pointer to select the number D.Alternatively, the user terminal can use a random number generator togenerate a random number between 0 and 9 and apply this number to selectD.

In one embodiment, the maximum value of random delay D is 9 symbols.Therefore, a user terminal can pick one of the 10 random delays, {0,1,2,. . . ,9} to send its CR burst to the base station. In addition, themaximum allowable roundtrip delay from the base station to the userterminal is assumed to be 50 symbols. Therefore, a CR burst can bedelayed as much as 59 symbols for a user terminal at the maximumpossible range. This delay is measured with respect to the CR burst of auser terminal that is at zero range and that did not delay itstransmission.

The base station receives and resolves the CR burst as described below.The roundtrip delay is determined to be 2(R/c)+D microseconds (since asymbol period is 2 microseconds where R km is the range of the userterminal. The base station, in the Configuration Message (CM) burst,then instructs the user terminal to advance its time by τ_(a)=(R/c+D/2)microseconds in its response to the CR burst. The base station isunaware of what, if any delay D the user terminal has applied to its CRburst. In response to this instruction, the user terminal, knowing itsrandom delay D will subtract out the random delay from the propagationdelay and advance its timing by τ_(a)-(D/2) microseconds.

The random delay of D symbols is particularly valuable in amicrocellular setting, or when user terminals cluster at about the samerange from the base station. If the range is about the same for twodifferent user terminals, the CR bursts from the two user terminals willlook identical at the base station and may not be resolved. With randomdelays, the CR bursts will be spaced apart making them easier todistinguish.

CR Burst Resolution

FIG. 5 shows a training sequence of a CR burst for one embodiment of theinvention. In FIG. 5, x510 is one of the two core sequences {s₁, s₂}. xis the vector consisting of 12 symbols x₁ to x₁₂. In this application,boldface text is used to represent vectors and normal text is used torepresent scalars. The complete CR Burst training sequence isconstructed from the core periodic sequence x. Nine repetitions of x;P1,P2, . . . , P9 are followed by a marker sequence M 505. FIG. 5 alsocan be viewed from the perspective of base station timing. In oneembodiment, FIG. 5 shows windows that the base station uses to resolvereceived training sequences in a CR burst. In this context, thesequences P1 to M would line up with the windows as shown only if thesequences were received from a user terminal that was in the samelocation as the base station, or in other words, if there were nopropagation delay between the base station and the user terminal. Inthis paradigm, a round trip delay margin window 520 contains thesequences P1 through P5 for a total of 60 symbols or 120 microseconds.This accommodates a combined delay of 50 symbols due to the round trippropagation delay between the user terminal and the base station and 10symbols of user terminal selected random delay. A beamformer analysiswindow 530 contains core sequences P6 through P9 and so is 48 symbolswide. This window will capture 4 periods of x even if the CR burst isdelayed by up to 60 symbols.

Using the observations that fall into the beamformer analysis window, abase station can estimate the delay encountered by the CR burstmodulo-12 symbols since each period P1 through P9 is identical and 12symbols long. In other words, the measurement in the beamformer analysiswindow will be the same for the delays τ and τ+12, where 0<τ<12. Themarker sequence M at the end of the burst can be used to resolve thismodulo-12 ambiguity.

In order to demodulate the payload part of the burst, the absolutetiming information instead of the relative timing or modulo-12 timinginformation is desired. As mentioned above, the marker sequence (M) atthe end of the training sequence of FIG. 5 can be used for this task.The marker sequence M is set to be M=−x so that one period of the coretraining sequence x augmented with M will be orthogonal to twoconcatenated periods of x, i.e., [x, M] [x,x]^(H)=0 in which x=[x₁, . .. , x₁₂], the core sequence, forms a period of the training sequence.

Since, in the present embodiment, the maximum allowed delay is 60symbols, a roundtrip delay margin window with a duration of 5 periods ofthe core sequence is provided. This leaves a duration of 4 periods ofthe core sequence for the beamformer analysis window. Absolute timing isdetermined by determining which of the four possible periods of the coresequence is the last one received before the marker sequence. Thebeamformer analysis window may contain portions of five different coresequences, at least three of which are full periods of the coresequence. The first symbol of the found sequence is either 12, 24, 36 or48 symbols from the first symbol of the marker sequence. Therefore theabsolute timing can be determined by testing only five hypotheses. Inother words, given τ, (0≦τ<12), as the modulo-12 delay estimate from thespatial processing search, the possible candidates for the absolutedelay are: {τ, τ+12, τ+24, τ+36, τ+48}.

As can be seen from FIG. 5, for any delay less than 60 symbols, thebeamformer analysis window at the base station will always contain atleast 4 periods of the periodic sequence x. As a result, the firstsymbol, x₁, of the first repetition of the core sequence within thebeamforming analysis window can be at most 12 symbols away from theborder of the round trip delay margin window and the beamformer analysiswindow.

This property of the repeating periodic training sequence can be takenadvantage of when searching for the first symbol, x₁, of the coresequence x. FIG. 6 shows a flow diagram for resolving the CR burstaccording to one embodiment of the invention. The CR burst is receivedat the antenna array 602 and the measurements from the multiple antennasfor the period that covers the beamformer analysis window are stored604. Then the beamforming weights that will yield the minimum leastsquares (LS) error for each timing hypothesis in the search window of 12symbols is determined. The least squares error results are used to finda coarse relative timing hypothesis 606. Finding this timing includesperforming a coarse search for the symbol timing modulo-12 andperforming a follow-up search 608.

A weight vector is then determined 610 using the relative timing. Thisweight vector is applied to the stored measurements to convert themeasurements from each antenna channel into a single channel 612. Then,this single channel is analyzed to determine the fine timing 614 and thefrequency offset 616 of the desired signal. The fine timing andfrequency estimates are used to determine a new more accurate weightvector 618 based on the data in the beamforming analysis window. Thisimproves the quality of the weight vector and the new weight vector isapplied to the stored measurements to convert the measurements from eachantenna channel into a new single channel 620, further improving thequality of the received signal. The processing so far cannot perfectlydetermine the timing information, because it can only measure timedelays modulo-12 symbols, the duration of the repeating core sequence.The timing estimate is in the range {0 . . . 12}, i.e., delays of τ andτ+12 symbols will ideally produce the same timing estimate at thispoint. Using the new weight vector, absolute timing is determined byfinding the marker sequence 622. This resolves the modulo-12 timingambiguity.

When the absolute timing is known, the entire training sequence can beidentified. Accordingly a new weight vector calculation can be madeusing the entire training sequence including the marker sequence 624.This redetermined weight vector is still more accurate because of thelarger number of samples that can be used. It is applied to the storedmeasurements to again convert the measurements from each antenna channelinto a single channel 626. With the new single channel, the CR burst isdemodulated and read 628.

This processing structure yields accurate beamformer weights that can beused to receive the desired signal without determining perfect timingfor the signal.

Coarse Search for Relative Timing

After the CR burst has been received in each of the antennas of thearray 602 and the signals have been stored 604. The system can proceedto determine the relative timing based on the stored measurements 606.In one embodiment, this process is done using a covariance matrixcomputation and a Cholesky decomposition.

For measurements that lie in the beamforming analysis window assume thatmeasurements are collected at 1.5 times the symbol rate. In thisexample, the beamforming analysis window is of duration 48 symbols or 4repetitions or periods of the core sequence. Next, assume that thevariable coreSnapPoint points to the first snapshot that is in thebeamformer analysis window, and r(t) denotes the snapshot (measurementvector) collected at time t seconds after the start of the CR burst(relative to base station time). The covariance matrix R can beestimated as follows, where T_(BAW) is the time of the beamforminganalysis window:${R = {\sum\limits_{t \in T_{BAW}}^{\quad}\quad {r\quad (t)\quad r^{H}\quad (t)}}},{T_{BAW} = \left\{ t \middle| {{coreSnapPoint} \leq t < {{coreSnapPoint} + 48}} \right\}}$

After computing the covariance matrix R, a matrix L can be found suchthat

R=L L^(H)

L is termed as the Cholesky factor of R.

In one embodiment, the location of the first symbol of the core trainingsequence over the first 12 symbols of the beamforming search window issearched for using a least-squares processor with a search step of 2/3symbols. This results in 18 possible locations of the first symbol, i.e.18 hypotheses and, accordingly, 18 least-squares (LS) errorcalculations. The vector coarseSearchGrid contains the delay hypothesisvalues for each 2/3 symbol increment (The unit used here is a symbolperiod):

coarseSearchGrid=[0,2/3,4/3,2, . . . , 11 1/3] which contains the delayvalues for the 18 hypotheses.

For each delay hypothesis k, (1≦k≦18), the following computations areperformed:

Calculate cross-correlation vector p_(k) for each hypothesis:$p_{k} = {\sum\limits_{t \in T_{BAW}}^{\quad}\quad {r\quad (t)\quad d*\left( {t + \tau_{k}} \right)}}$

In which r(t) is the received signal samples and d(t) is the samples ofthe desired signal. The desired signal samples are assumed to beavailable in a filter bank over-sampled at 24 times the symbol rate. Thevalue τ_(k) is the assumed delay for the k-th hypothesis, i.e.,τ_(k)=coarseSearchGrid (k).

Back Substitution: The resulting vector p_(k)is applied to solve for aninterim vector x_(k) for each hypothesis k, where L is the Choleskyfactor as mentioned above:

Lx_(k)=p_(k)

Then the least-squares (LS) fit for each hypothesis is computed:$f_{k} = {{f\quad \left( \tau_{k} \right)} = {{\sum\limits_{t \in T_{BAW}}^{\quad}\quad {{d\quad \left( {t + \tau_{k}} \right)}}^{2}} - {X_{k}^{H}\quad X_{k}}}}$

Due to the periodicity of the desired signal within the beamforminganalysis window, the cross correlation vector computation can bemodified to:$p_{k} = {\sum\limits_{t \in T_{1}}^{\quad}\quad {\left\lbrack {{r\quad (t)} + {r\quad \left( {t + 12} \right)} + {r\quad \left( {t + 24} \right)} + {r\quad \left( {t + 36} \right)}} \right\rbrack \quad d*\left( {t + \tau_{k}} \right)}}$

in which T₁ is a period of the desired signal, i.e.,

T₁={t|coreSnapPoint≦t≦coreSnapPoint+12}

Therefore, the above calculation of the cross correlation vector p_(k)costs one-fourth as many multiplies as it would if the core sequencewere not a repeated periodic sequence within the training sequence.Finally, the hypothesis with the minimal LS error f_(k) is picked. Anillustration is presented with respect to FIG. 7.

FIG. 7 shows the LS cost function on the vertical axis 702 as a functionof the time delay τ for the 18 hypotheses on the horizontal axis 704.The horizontal axis is marked in units of 2/3 of a symbol time in accordwith the sampling rate of 1.5 times the symbol rate. The selected bestcoarse search time delay estimate 706 is shown in FIG. 7 at τ=4/3symbols. Note that the delay is measured with respect to the nominaltime or modulo-12 time at which the CR burst is expected to arrive. Thisnominal time is named the coreSnapPoint. This simplified computation ofthe cross correlation vectors p_(k) based on the periodicity of thetraining sequence within the beamforming analysis window yieldssubstantially the same accuracy as a regular cross correlationcomputation. Any mismatch of the training sequence in this simplifiedapproach makes only a minimal impact on the performance of thebeamformers due to the periodicity of the training sequence.

Follow-up Search

Having made a coarse determination of the relative timing 606 afollow-up timing search 608 can be performed. This search has one moreLS error calculation. The result of this calculation can be compared tothe best LS error from the coarse search.

The LS error vector f_(k) from the coarse search is treated as acircular buffer and concentration is on the midpoint of the rangebetween the best location from the coarse search (that yielded theminimum LS error) and its neighbor that yielded the next best LS error.

In the coarse search, the following 20 dimensional vectors were formed:

updatedLSValues=[f₁₈,f₁,f₂,f₃,f₄, . . . , f₁₇,f₁₈,f₁]

and

updatedCoarseSearchGrid=[−2/3,0,2/3,4/3,3 1/3, 4, . . . , 11 1/3, 12]

Assume that the hypothesis of f₃ (τ=4/3) (of the current list) wasselected by the coarse search procedure (as shown in FIG. 5) becausef₃<f₂<f₄. In the follow-up search procedure, the LS error is computedfor τ=1, since this forms the midpoint of the range between the delayscorresponding to f₂(τ=2/3) and f₃(τ=4/3). This is shown graphically inFIG. 8.

FIG. 8 shows the LS cost function 802 as a function of the 18 hypotheses804 in which the time domain is again sampled at a rate of 1.5 times thesymbol rate. The selected best case coarse search time delay estimate806 is τ=4/3 symbols. After the additional hypothesis test, thehypothesis (among the 19 of them) which corresponds to the minimumleast-squares error is again picked. In this example, τ_(o)=1 is thedelay value 808 that accomplishes this.

Beamforming Weights

After the follow-up search, determining the relative timing delay τ towithin one third of a symbol period 608, the weight vector w_(o) isrecomputed to extract the desired signal as follows:

Using the cross-correlation vector p_(o) for the best hypothesis:$p_{0} = {\sum\limits_{t \in T_{BAW}}^{\quad}\quad {r\quad (t)\quad d*\left( {t + \tau_{o}} \right)}}$

And the corresponding interim vector x_(o):

Lx_(o)=p_(o)

The weights can be computed by solving the following back substitution:

L^(H)w_(o)=P_(o)

With the resulting LS error which is already determined to be f(τ_(o)):${f\quad \left( \tau_{o} \right)} = {{\sum\limits_{t \in T_{BAW}}^{\quad}\quad {{d\quad \left( {t + \tau_{o}} \right)}}^{2}} - {x_{o}^{H}\quad x_{o}}}$

The beamforming operation results in a single channel measurement thatshall be named g(t) and defined as follows:

g(t)=w_(o) ^(H)r(t)

The actual computations can be simplified because the time range of thebeamforming operation does not need to be the whole burst. Note that thefrequency estimation (search) has not yet been performed. This reducesthe search to a single dimension, namely time-delay. The frequencysearch can be avoided because of the duration of the beamforminganalysis window, the maximum frequency deviation expected in thereceived signal and the target SNR level at the output of thebeamformer. When the beamformer analysis window is short enough to makethe frequency offset negligible, the desired signal mismatch is notsignificant enough to degrade performance. Furthermore, the inability toimprove the SNR even by using an MSE beamformer (that knows the perfectcovariance matrix and steering vector) to high levels (above 5 dB) makesthe actual beamformer blind to imperfections in the desired signal (suchas frequency offset). The presence of frequency offset becomes seriousat high target SNRs and ignoring large frequency offsets causes the SNRperformance to tend to saturate at around 5 dB output SNR. However, thisis still not an issue if the CR burst payload can withstand SNRs as lowas 0 dB. Furthermore, the single channel estimation of frequency andfine timing that follows will alleviate these problems using fewercomputations.

Fine Timing Estimator

The coarse search and the follow-up search provide a timing delay withan effective rate of three times the symbol rate. The timing resolutioncan be improved to better demodulate the payload. Severe intersymbolinterference can be expected at the worst case timing events (1/6 symbolperiod of timing error). To estimate fine timing 614, the Oerder-Meyrblind timing estimator can be used. This estimator is blind in the sensethat it does not assume any knowledge of the transmitted symbols.Therefore it is insensitive to frequency offset errors. The Oerder-Meyrestimator can be used as follows:

First, interpolate g(t) to 3 times the symbol rate (from 1.5 times thesymbol rate) using an interpolation filter, and call the outputg_(i)(t). The duration of the measurements process amounts to48+12+82=144 symbol periods, this is the guaranteed maximum number ofsymbols on the right hand side of the coarse timing estimate in thebeamforming analysis window as shown in FIG. 5. Alternatively, thesymbols can be sampled at a three times rate originally. In such a case,only every other sample would be used in the coarse search and follow-upsearch.

Next, the interpolated signal is passed through a memorylessnonlinearity to obtain

g _(n)(t)=|g _(i)(t)|.

The absolute value nonlinearity generates tones at the multiples of thesymbol rate. The nonlinearity is approximated by fitting a polygon. Forexample, if z is a complex number with representation z=z_(r)+jz_(i),then |z|≈max(|z_(r)|,|z_(i)|)+0.34×min (|z_(r)|,|z_(i)|). Thezero-crossing of the complex sine wave at the symbol rate is determinedby using a 3 point DFT and this location is termed as a symboltransmission instant. Finally, the symbol transmission instant is foundthat is closest to the position identified by the follow-up search asthe location for the first symbol of the periodic training sequence.

The closed-form estimate obtained using the Oerder-Meyr timing estimatoris termed as τ_(fine) If this estimate is not in the range (0,12), it ismapped into this range by adding or subtracting 12 to it.

Coarse Frequency Estimator

After fine timing is acquired 614, the measurements are used in theanalysis window together with the desired signal to compute the crosscorrelation function and determine the coarse frequency estimate 616 asthe peak of the cross correlation function. For simplicity, thisanalysis is done at the 1.5 times over sampling rate (instead of the 3times rate used for the fine timing search), however many other samplingrates can be used. Specifically, for the m-th frequency hypothesis, thefunction freqMatch(m) is computed:${{freqMatch}\quad (m)} = {{\sum\limits_{t \in T_{BAW}}^{\quad}\quad {g\quad (t)\quad d*\left( {t + \tau_{fine}} \right)\quad \exp \quad \left( {{- j}\quad 2\quad \pi \quad f_{m}\quad t} \right)}}}^{2}$

The frequency candidate that maximizes freqMatch(m) is selected as thefrequency estimate, fcoarse Frequency candidates (f_(m)′s) are in theset:

{−2800,−2000,−1200,−400,400, 1200, 2000,2800}

Alternatively, the frequency uncertainty can be regarded as much lessand fewer hypothesis tests can be performed.

More Accurate Beamforming

Using the frequency and timing estimates t_(fine), f_(coarse), animproved weight vector, w_(final) can be determined 618 and applied tothe found core sequences to obtain an estimate of the desired burstŝ(t):

ŝ(t)=w_(final) ^(H) r(t)

The more accurate weight vector is obtained by employing d(t+τ_(fine))exp (j2πf_(fine)t) as the desired signal in the LS error computations.However, if the corresponding LS error is larger than the follow upsearch based LS error f_(o), the fine timing and frequency estimates arerejected and the estimates are set to τ_(fine)=τ_(o) and f_(coarse=)0,which results in w_(final)=w_(o).

To further improve the SNR results at high post-copy SNR levels, thesearch can be performed for a fine frequency estimate around the coarsefrequency estimate at locations f_(coarse)+[−800,0,800] using an LS fitto multichannel measurements for t εT_(BAW). Such a search can beincluded to improve the frequency estimation performance for the CRburst demodulator.

Absolute Timing Recovery

Prior to determining the absolute timing, as opposed to relative timing,the more accurate weight vector is applied in order to convert themeasurements stored from each of the antennas into a single channelmeasurement 620. This conversion is still done using the data in thebeamforming analysis window because only this data is certain to consistonly of periods of the core sequence. An appropriate procedure 622 fordetermining the absolute delay can be implemented as follows. Assumethat the modulo-12 time-delay estimate is τ, and that g(t) denotes theoutput of a beamformer (as described above g(t) is a single channelmeasurement) that extracts the desired CR burst. First, the candidatestarting locations for the concatenated sequence [P9,M] (see FIG. 5) foreach of the five delay hypotheses is determined. For example, if theabsolute delay equals τ, the sequence [P9,M] should start τ+36 symbolsaway from the left border of the beamformer analysis window. For thehypothesis in which the absolute delay is assumed to be equal to τ+48,the sequence [P9, M] should start τ 84 symbols away from the left borderof the analysis window.

More specifically, assume that T_(k) denotes the begin time for the k-thhypothesis, i.e., T_(k) =τ+36 +(12×k), for k=0, 1,2,3,4. Let v_(k)denote the samples of g(t) that correspond to the interval which startsat T_(k) for a duration of 24 symbols (two periods). For eachhypothesis, compute:

h(k)=|v _(k) [x,−x] ^(H)|².

Pick the hypothesis that yields the maximum h(k).

Assume that hypothesis k_(o) is selected. Then, the absolute timingestimate is determined as τ+(k_(o)×12).

Due to the orthogonal nature of [x, m] and [x, x], there is a five-arypulse-position modulation (PPM) demodulation problem in which the SNRchanges depending on the true position of the desired vector [x, m]. Forexample, if the actual delay is less than a period, then the payloadportion of the desired CR burst will appear as noise for the hypothesistests 1,2,3,4. On the other hand, if the actual delay is, for example 20symbols, then, the CR burst payload symbols will not contribute to thetest of a hypothesis in which k=0 as noise because of the orthogonalityof [x, m] and [x, x], but they will contribute to the noise component inh(k) for k=2,3,4. With this delay condition, the beamforming analysiswindow receives the following 48 symbols:

x₅,x₆,x₇,x₈,x₉,x_(10,x) ₁₁,x₁₂,x₁,x₂,x₃,x₄, . . .x₅,x₆,x₇,x₈,x₉,x₁₀,x₁₁,x₁₂,x₁,x₂,x₃,x₄,

In this stream, the first and last 12 symbols are written out. Thespatial processing search will discover the first occurrence of x_(i) ata delay of 8 symbols. The next step is to determine whether the absolutedelay is 8,20,32,44,56 symbols. In order to determine this, themeasurements following the beamforming analysis window are focused upon.With a delay of 20 symbols, the next 40 symbols will be:

x₅,x₆,x₇,x₈,x₉,x₁₀,x₁₁,x₁₂,x₁,x₂,x₃,x₄,x₅,x₆,x₇,x₈,x₉,x₁₀,x₁₁,x₁₂,−x₁,−x₁,−x₂,−x₃,−x₄,−x₅,−x₆,−x7,−x8,−x₉,−x₁₀,−x₁₁,−x₁₂,d₁,d₂,d₃,d₄,d_(5,d) ₆,d₇,d₈

in which d_(i) indicates the i-th payload symbol, which is unknown. As aresult, v₀=[x, x] and v₁=[x, −x], which results in h(0)=0 and h(1)=24².Accordingly, the desired signal does not contribute to the decisionvariable h(0) when the absolute delay is larger than 12. On the otherhand, v₂=[−x₁,−x₂, . . . ,−x₁₂, d₁,d₂, . . . d₁₂] is not necessarilyequal to zero. The first half of v₂ equals the marker sequence, whichyields the result:

h(2)=|−12−[d ₁ ,d ₂ , . . . d ₁₂ ]x ^(H)|².

This differs significantly from:

h(3)=|[d ₁ ,d ₂ , . . . d ₁₂ ]x ^(H) −[d ₁₃ ,d ₁₄ , . . . , d ₂₄ ]x^(H)|².

h(2) is expected to be higher than h(3) on average because of thecoherence term (−12) inside the magnitude operator and its presencecreates a significant competition to the correct hypothesis decisionvalue (h(0)) in the presence of measurement noise. Therefore, absolutedelay errors that are equal to +12 should dominate other values of delayestimation errors. One way to eliminate the self-noise problem is to putthe marker sequence in the beginning of the burst and search for theconcatenated sequence [−x, x]. In such a design, self noise will existonly due to the presence of the ramp-up symbols, but this will affectthe noise component in only one of the h(k)'s. Other modifications tothe ordering of the sequences are also possible to suit particularapplications.

As discussed above, the remaining task is to find the marker sequence.This can be done based on a cross correlation operation with the 1.5times over-sampled version of the sequence [x,−x] with v_(k)corresponding to all of the five hypotheses locations indicating periodslips of 0,1,2,3,4.

Using the fine timing estimate τ_(fine), the time of the finalbeamformer output sample (that arrives at t_(c)) which is closest tocoreSnapPoint+τ_(fine) is determined. Let τ_(e) denote the timedifference between the chosen measurement at t_(c) and the location ofactual timing location:

τ_(e) =t _(c)−coreSnapPoint−τ_(fine)

Remember that the beginning of the k-th hypothesis (k=0,1,2,3,4) will beat times T_(k)=coreSnapPoint+τ_(fine). Therefore, the vector v_(k) to betested for the cross correlation for the k-th hypothesis will take theform:

v _(k) =[ŝ(t _(c)+12×(3+k)), ĝ(t _(c)+12×(3+k)+2/3)],

ŝ(t _(c)+12×(3+k)+2×2/3), . . . ŝ(t_(c)+12×(3+k)+35×2/3)

which is a vector with 36 entries.

The v_(k)'s are cross correlated with the desired signal vector d, whichis formed from the knowledge of the training waveform and the timingdifference τ_(e):

 d=[s _(d)(coreSnapPoint+τ_(e)+12×3), s_(d)(coreSnapPoint+τ_(e)+12×3+2/3), . . . , s_(d)(coreSnapPoint+τ_(e)+12×3+35×2/3)]

in which s_(d)(t) is the training waveform for the desired signal.

The magnitude squared cross correlations for each hypothesis iscomputed:

h(k)=|v_(k) d ^(H)|²

Let k_(o) denote the index of the largest h(k). Then, the absolutetiming is determined as:

τ_(abs)=τ_(fine)+(k _(o)×12)

The values are in terms of symbol durations in the above equation withthe period of the training sequence being 12 symbols.

Alternatively, symbol spaced sampling can be used in the absolute timingrecovery. This can eliminate the mismatches created in the 1.5 timesmeasurements that result in loss of orthogonality. With symbol spacedsampling, this operation will require 5 cross correlations of length 24and comparing the squared-magnitudes of the cross correlations.

After absolute timing recovery 622, the whole training sequence can beused to improve the timing and frequency estimates and these estimatescan be used to perform one more stage of beamforming over the wholetraining sequence duration. This can increase the number of symbols usedin spatial processing to 120 symbols from 48 and improve the performanceat a cost of computational complexity The beamforming would involvefirst determining a still more accurate weight vector using the fulltraining sequence 626 and then applying this weight vector to convertthe measurements stored for each antenna channel into a single channelmeasurement 628. In doing so a new covariance matrix should be computedand therefore another Cholesky factorization performed. The conversioncan be applied to the entire CR burst so that the CR burst can bedemodulated as a single channel 628. Alternatively, the absolute timingcan be applied to determine the beginning and end of the CR burst andthe existing weight vector and frequency estimates can be used todemodulate the signal. The choice will depend on the demands of theparticular system and the condition of the channel. Having determinedtiming and a weight vector, this weight vector can be used to sendtraffic back to the remote from which the CR burst was received 630.

General Matters

The present invention can eliminate the need to acquire the absolutetiming information in order to perform beamforming. It exploits theperiodicity of target training sequences in order to estimate the timedelay encountered by the desired signal modulo-the period of thetraining sequence which is less than the total time delay ambiguityrange. The reception of uplink messages at the base station which arenot perfectly synchronized is enhanced.

Training based interference cancellation methods can be used to enhancethe signal quality for such bursts. However, the training sequenceshould be aligned with the incoming signal, and therefore the resultingsearch process involves testing every possible delay with apredetermined resolution. As the delay ambiguity grows, this hypothesistesting process becomes increasingly more expensive with computationalresources.

Using a periodic training sequence eases the efforts of hypothesistesting followed by a timing acquisition sequence to determine theperfect timing information. The periodic sequence decreases the timingambiguity to within a period of the training sequence, which can beselected small so that resources are available to handle the hypothesistesting task. For example, if the expected delay is 50 symbols, and ifthe period of the training sequence is 10 symbols, with a resolution ofa symbol, 10 hypotheses can be tested instead of 50, provided that theperiodic training sequence can be observed in the search window,regardless of the delay. In addition, the search operation, whichinvolves cross correlations can be simplified by the number of periodsin the search window, if the search window contains 5 periods of thetraining sequence (period with 10), the cross correlations can besimplified by five-fold.

Once the timing hypothesis is verified, only the number of periods ofthe repeating core sequence that has been skipped must be determined. Toperform this more accurately, the multiple channel measurements (ifavailable) can be converted to a single channel measurement using thesearch procedure results outlined above. After that a timing acquisitionsequence that is at the beginning of the burst can be found, and to findthe number of periods that were missed. So in the previous example, onlyperiods {0,1,2,3,4} may have been missed in the beamforming analysiswindow. Accordingly, 5 searches can be performed and these are performedon single channel measurements rather than multichannel measurements.

The invention eliminates the high cost of search on possiblymultichannel data for all possible delays that may be encountered by theuser terminal as a function of range. The burst structure and periodictraining sequence makes it easier to search for the arrival time of thesignal and the periodicity of the training further reduces the cost ofcomputations.

In the description above, for the purposes of explanation, numerousspecific details are set forth in order to provide a thoroughunderstanding of the present invention. It will be apparent, however, toone skilled in the art that the present invention may be practicedwithout some of these specific details. In other instances, well-knownstructures and devices are shown in block diagram form.

The present invention includes various steps. The steps of the presentinvention may be performed by hardware components, such as those shownin FIGS. 1 and 2, or may be embodied in machine-executable instructions,which may be used to cause a general-purpose or special-purposeprocessor or logic circuits programmed with the instructions to performthe steps. Alternatively, the steps may be performed by a combination ofhardware and software. The steps have been described as being performedby either the base station or the user terminal. However, any stepsdescribed as being performed by the base station may be performed by theuser terminal and vice versa. The invention is equally applicable tosystems in which terminals communicate with each other without eitherone being designated as a base station, a user terminal, a remoteterminal or a subscriber station.

The present invention may be provided as a computer program productwhich may include a machine-readable medium having stored thereoninstructions which may be used to program a computer (or otherelectronic devices) to perform a process according to the presentinvention. The machine-readable medium may include, but is not limitedto, floppy diskettes, optical disks, CD-ROMs, and magneto-optical disks,ROMs, RAMs, EPROMs, EEPROMs, magnet or optical cards, flash memory, orother type of media/machine-readable medium suitable for storingelectronic instructions. Moreover, the present invention may also bedownloaded as a computer program product, wherein the program may betransferred from a remote computer to a requesting computer by way ofdata signals embodied in a carrier wave or other propagation medium viaa communication link (e.g., a modem or network connection).

Importantly, while the present invention has been described in thecontext of a wireless internet data system for portable handsets, it canbe applied to a wide variety of different wireless systems in which dataare exchanged. Such systems include voice, video, music, broadcast andother types of data systems without external connections. The presentinvention can be applied to fixed remote terminals as well as to low andhigh mobility terminals. Many of the methods are described in their mostbasic form but steps can be added to or deleted from any of the methodsand information can be added or subtracted from any of the describedmessages without departing from the basic scope of the presentinvention. It will be apparent to those skilled in the art that manyfurther modifications and adaptations can be made. The particularembodiments are not provided to limit the invention but to illustrateit. The scope of the present invention is not to be determined by thespecific examples provided above but only by the claims below.

What is claimed is:
 1. A method comprising: receiving a burst from aterminal at a set of spatial diversity antennas, the burst including aknown training sequence; storing measurements of the received burst fromeach spatial diversity antenna corresponding to receive times within aselected analysis window; determining weights for each diversity antennafor at least a portion of the training sequence of the burst beforetiming for the burst has been determined; applying the determinedweights to the stored measurements; and determining timing for the burstbased on the stored measurements to which the determined weights havebeen applied.
 2. The method of claim 1 wherein determining weightscomprises selecting weights that will yield a minimum least squareserror for at least a portion of the training sequence of the burst. 3.The method of claim 1 wherein the weights relate to the spatialdirectionality and interference of the received burst.
 4. The method ofclaim 1 further comprising applying the determined timing to the burstand redetermining weights that will yield a minimum least squares errorfor the burst using the determined timing.
 5. The method of claim 4further comprising applying the redetermined weights to at least aportion of the burst and redetermining timing using the at least aportion of the burst to which the redetermined weights have beenapplied.
 6. The method of claim 5 further comprising determiningfrequency offset using the at least a portion of the burst to which theredetermined weights have been applied.
 7. The method of claim 5 furthercomprising applying the redetermined timing to the burst and furtherdetermining weights that will yield a minimum least squares error forthe burst using the redetermined timing.
 8. The method of claim 5wherein computing a covariance matrix comprises computing a covariancematrix only for a portion of the known training sequence.
 9. The methodof claim 1 further comprising generating a single representation of thereceived burst after applying the determined weights.
 10. The method ofclaim 9 wherein determining timing further comprises calculating a crosscorrelation vector for the plurality of different timing hypotheses forapplication to the least squares calculation.
 11. The method of claim 1wherein determining the weights comprises computing a covariance matrixagainst the expected signal.
 12. The method of claim 1 whereindetermining timing comprises determining a least squares error for aplurality of different timing hypotheses for a portion of the knowntraining sequence.
 13. The method of claim 1 wherein determining timingcomprises determining timing with respect to a repeated core sequence ofthe known training sequence and then determining timing with respect tothe entire received burst.
 14. The method of claim 13 further comprisingredetermining weights using the entire received burst after determiningtiming with respect to the entire received burst.
 15. The method ofclaim 1, wherein the burst is configured in accordance with at least oneof a TDMA, a FDMA, a CDMA and a FDD air interface standard.
 16. Amachine-readable medium having stored thereon data representingsequences of instructions which, when executed by a machine, cause themachine to perform operations comprising: receiving a burst from aterminal at a set of spatial diversity antennas, the burst including aknown training sequence; storing measurements of the received burst fromeach spatial diversity antenna corresponding to receive times within aselected analysis window; determining weights for each diversity antennafor at least a portion of the training sequence of the burst beforetiming for the burst has been determined; applying the determinedweights to the stored measurements; and determining timing for the burstbased on the stored measurements to which the determined weights havebeen applied.
 17. The medium of claim 16 wherein the instructionscausing the machine to perform operations comprising determining weightsfurther comprise instructions for selecting weights that will yield aminimum least squares error for at least a portion of the trainingsequence of the burst.
 18. The medium of claim 16 further comprisinginstructions causing the machine to perform operations comprisingapplying the determined timing to the burst and redetermining weightsthat will yield a minimum least squares error for the burst using thedetermined timing.
 19. The medium of claim 18 further comprisinginstructions causing the machine to perform operations comprisingapplying the redetermined weights to at least a portion of the burst andredetermining timing using the at least a portion of the burst to whichthe redetermined weights have been applied.
 20. The medium of claim 18further comprising instructions causing the machine to performoperations comprising determining frequency offset using the at least aportion of the burst to which the redetermined weights have beenapplied.
 21. The medium of claim 18 further comprising instructionscausing the machine to perform operations comprising applying theredetermined timing to the burst and further determining weights thatwill yield a minimum least squares error for the burst using theredetermined timing.
 22. The medium of claim 16 wherein the instructionscausing the machine to perform operations comprising determining theweights further comprise instructions to compute a covariance matrixagainst the expected signal for a portion of the known trainingsequence.
 23. The medium of claim 16 wherein the instructions causingthe machine to perform operations comprising determining timing furthercomprise instructions for determining a least squares error for aplurality of different timing hypotheses for a portion of the knowntraining sequence.
 24. The medium of claim 16 wherein the instructionscausing the machine to perform operations comprising determining timingfurther comprise instructions for determining timing with respect to arepeated core sequence of the known training sequence and thendetermining timing with respect to the entire received burst.
 25. Themedium of claim 16, wherein the burst is configured in accordance withat least one of a TDMA, a FDMA, a CDMA, and a FDD air interfacestandard.
 26. An apparatus comprising: a set of spatial diversityantennas at a terminal to receive a burst, the burst including a knowntraining sequence; a memory to store measurements of the received burstfrom each spatial diversity antenna corresponding to receive timeswithin a selected analysis window; a processor to determine weights foreach diversity antenna for at least a portion of the training sequenceof the burst before timing for the burst has been determined to applythe determined weights to the stored measurements, and to determinetiming for the burst based on the stored measurements to which thedetermined weights have been applied.
 27. The apparatus of claim 26wherein the processor further applies the determined timing to the burstand redetermines weights that will yield a minimum least squares errorfor the burst using the determined timing.
 28. The apparatus of claim 27wherein the processor further applies the redetermined weights to atleast a portion of the burst and redetermines timing using the at leasta portion of the burst to whichfihe redetermined weights have beenapplied.
 29. The apparatus of claim 27 wherein the processor furtherdetermines frequency offset using the at least a portion of the burst towhich the redetermined weights have been applied.
 30. The apparatus ofclaim 27 twherein the processor determines timing with respect to arepeated core sequence of the known training sequence and thendetermines timing with respect to the entire received burst.
 31. Theapparatus of claim 26, wherein the terminal is within at least one of aTDMA, a FDMA, a CDMA and a FDD radio communications system.